DWNTs are in the strong coupling regime when the constituting tubes' chiral vectors are nearly parallel and their difference points along the armchair direction.
DWNTs consisting of armchair tubes (n,n)@(m,m) fulfill both conditions.
Armchair single-wall nanotubes (SWNT)
present two nearly linear bands crossing at the Fermi energy, resulting in a metallic system with 2 conductance [1]}, [2]}. Without interlayer interaction, the band structure and conductance of an ideal DWNT would simply be the sum of the individual SWNT ones.
Deviations from the ideal case can only occur for perturbations of the sidewalls, for instance due to defects [3]}, [4]} or functionalization [5]}, [6]}.
The infinite (10,10)@(15,15) DWNT, instead, features (Fig. REF b) a subtle band structure of states localized on either tube (positive Fermi velocity, red/blue) and hybridized states (negative Fermi velocity, gray). The conductance of the DWNT with finite overlap region shows a maximum of 1 computed in the set-up of Fig. REF a.
The transmission function presents a series of dips where conduction is blocked (Fig. REF c). The number, position and width of the dips depend on \(L\)  (Fig. REF a). Each of these dips corresponds to a localized eigenstate in the overlap region (Fig. REF c horizontal lines).
At \(L\approx {50}{}\)  and \(L\approx {150}{}\)  the dips in transmission are barely visible. At intermediate overlap lengths, the interlayer conductance is reduced, the dips are broader, and transmission is blocked completely for \(L\approx {100}{}\)  and
\(L\approx {200}{}\) , following a periodic behavior.
This reduction of the maximum conduction as well as the oscillation with overlap length was predicted in Ref. Tamura2005, and we can now show that localized states cause the dips observed in the conductance at fixed overlap lengths. We further show that the modulation of the transmission can be observed in a wide range of energy and overlap lengths.
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